Wow, doing a search on 60hz just comes up with a bunch of responses regarding registry tweaking and the 2K / XP 60hz bugs as far as I see. Skimming them over, I don't see any that actually present the right solution. Rather than just saying to search and being "31337", let's actually work towards a solution.
The problem lies in that the Radeon, for some reason, relies on PnP information from your monitor to detect its highest resolution and refresh rate. If it can't detect that information for some reason, it limits you as to the resolutions and refresh rates that you can set, even though it'll allow you to select them (and for that matter, will make Windows think you did set them right). I was pulling my hair out on this one for the first day I had my Radeon, but I found the solution in the advanced settings.
Go to display properties, click on settings, and then click on advanced. In the window that pops up, click on the attributes tab. Then select the right maximum resolution for your monitor and the maximum refresh rate that it can handle (not the highest refresh rate it can handle in the highest resolution). For example, my monitor handles 160hz @ 640X480 and 70hz @ 1600X1200, thus I set the maximum resolution box to 1600X1200 and the maximum refresh rate box to 160hz, not to 1600 and 70). Click apply and OK to all the boxes, then try to set your resolution and refresh rate again. Now you should have the right refresh.
LMK if this works / doesn't work.
Shawn